A certain store sells small, medium, and large toy trucks in each of the colors red, blue green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
A. 1/4
B. 1/3
C. 1/2
D 7/12
E. 2/3
OA:C
Here is how I solved this problem. Total number of different trucks: 4x3 = 12 . Probability we are looking for: P(red OR medium) + P(red AND medium) = (3/12 + 4/12 -1/12) + (1/12) = 7/12. But my answer is wrong. Can anyone help me figuring out why? Thanks!
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
probability problem
This topic has expert replies
-
aneesh.kg
- Master | Next Rank: 500 Posts
- Posts: 385
- Joined: Mon Apr 16, 2012 8:40 am
- Location: Pune, India
- Thanked: 186 times
- Followed by:29 members
When you use the formula of
P(Red OR Medium) = P(Red) + P(Medium) - P(Red AND Medium)
it includes the trucks are Red but not Medium, Medium but not Red and Red and Medium.
So,
P(Red OR Medium) = (3/12 + 4/12 - 1/12) = 1/2 is the answer.
There is no need to add P(Red AND Medium) because it is already included above.
P(Red OR Medium) = P(Red) + P(Medium) - P(Red AND Medium)
it includes the trucks are Red but not Medium, Medium but not Red and Red and Medium.
So,
P(Red OR Medium) = (3/12 + 4/12 - 1/12) = 1/2 is the answer.
There is no need to add P(Red AND Medium) because it is already included above.
Aneesh Bangia
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
-
mcdesty
- Master | Next Rank: 500 Posts
- Posts: 116
- Joined: Wed Mar 14, 2012 1:02 pm
- Thanked: 20 times
- Followed by:11 members
- GMAT Score:760
My scratch paper looked like this when I solved this one.
- Attachments
-
I have made your mistakes before.
I am experienced - I have tutored calculus and linear algebra for over two years.
For a very modest fee, I will ensure that your GMAT journey is a smooth one: Daily assignments and careful micro management.
PM me so we can get started.
I am experienced - I have tutored calculus and linear algebra for over two years.
For a very modest fee, I will ensure that your GMAT journey is a smooth one: Daily assignments and careful micro management.
PM me so we can get started.
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
This appears to be another question in which the original posters are long since gone. It can be solved with a real simple "brute force" approach.
There are 3 types of toy trucks (small, medium and large) and 4 colors (red, blue, green and yellow).
We're told that there are equal numbers of each color-size combination and we're asked what the probability is of randomly pulling a truck that is RED or MEDIUM or BOTH.
I'm going to list out all of the possibilities and put a * next to the ones that fit what we're looking for:
Small Red *
Small Blue
Small Green
Small Yellow
Medium Red *
Medium Blue *
Medium Green *
Medium Yellow *
Large Red *
Large Blue
Large Green
Large Yellow
6 of the 12 options are red or medium or both.
Final Answer: [spoiler]6/12 = 1/2 = C[/spoiler]
GMAT assassins aren't born, they're made,
Rich
This appears to be another question in which the original posters are long since gone. It can be solved with a real simple "brute force" approach.
There are 3 types of toy trucks (small, medium and large) and 4 colors (red, blue, green and yellow).
We're told that there are equal numbers of each color-size combination and we're asked what the probability is of randomly pulling a truck that is RED or MEDIUM or BOTH.
I'm going to list out all of the possibilities and put a * next to the ones that fit what we're looking for:
Small Red *
Small Blue
Small Green
Small Yellow
Medium Red *
Medium Blue *
Medium Green *
Medium Yellow *
Large Red *
Large Blue
Large Green
Large Yellow
6 of the 12 options are red or medium or both.
Final Answer: [spoiler]6/12 = 1/2 = C[/spoiler]
GMAT assassins aren't born, they're made,
Rich
-
mcdesty
- Master | Next Rank: 500 Posts
- Posts: 116
- Joined: Wed Mar 14, 2012 1:02 pm
- Thanked: 20 times
- Followed by:11 members
- GMAT Score:760
I am not responding to the original poster.[email protected] wrote:Hi All,
This appears to be another question in which the original posters are long since gone.
I encourage the students I work with to make use of the forum: If one of them asks me a question, I post the solution on here so he/she can see how others approached the problem and adopt the best approach.
I have made your mistakes before.
I am experienced - I have tutored calculus and linear algebra for over two years.
For a very modest fee, I will ensure that your GMAT journey is a smooth one: Daily assignments and careful micro management.
PM me so we can get started.
I am experienced - I have tutored calculus and linear algebra for over two years.
For a very modest fee, I will ensure that your GMAT journey is a smooth one: Daily assignments and careful micro management.
PM me so we can get started.
